Tagged Questions

In cryptography, a discrete logarithm is the number of times a generator of a group must be multiplied by itself to produce a known number. By choosing certain groups, the task of finding a discrete logarithm can be made intractable.

Assuming a randomize encoding scheme that takes as input a secret key $\mathsf{sk} \in \mathbb{Z}_p$ for a large prime number $p$. Then the algorithm outputs $g^{\mathsf{sk}x}, x \in \mathbb{Z}_p^*$. ...

Crypto noob here, I am attempting to do this programming challenge. I do not have the secret key that is used to decrypt the message. However, the key is small enough for a brute force approach. I am ...

Given a field $\mathbb{F}_{2^n}$, are there any choices of primitive element $g$ that make the discrete logarithm easier for that generator? That is, are there any degenerate cases?
For example, if I ...

I'm trying to resolve a discrete logarithm equation:
$$y = g^x \bmod p$$
Every parameter is a 512-bit number. I know the values for $g$, $y$ and $p$ and I need to find the $x$ value. Finally, I know ...

From wikipedia, the DDH assumption says，given a cyclic group $G$ of order $q$ with generator $g$, $(g^a, g^b, g^{ab})$ looks like $(g^a, g^b, g^c)$ where $a,b,c$ are randomly and independently chosen ...

I was reading 'Pinocchio Coin' paper by Danezis et al. where they have said,
"If we use the efficient pairing groups of Pinocchio, computing discrete logarithms in the exponent field $\mathbb{F}_p$ ...

I am studying (sliding) window method in Elliptic Curve Cryptography (ECC) but I am confused by the term, signed fixed window method. By the way term is used in a research paper and not in the book ...

Take a cyclic group of prime order. The Schnorr-protocol for proving knowledge of the discrete logarithm of some group element is honest-verifier zero-knowledge, meaning that if the verifier chooses ...

Here $g$ is some fixed generator of a discrete log group. I don't want the group to be bilinear for efficiency and BDH-skepticism reasons.
Is anyone aware of a discrete log accumulator? What I mean ...

I am a bit confuse about the term, variable-base point/scalar multiplication, in Elliptic Curve Cryptography. What I have understood so far. It means that the base or point on EC is variable/unknown.
...

Assume you have a finite group $\mathbb{G}$ and an integer $n$. Given $g_1,\dots,g_n,t$ chosen uniformly from $\mathbb{G}$, consider the problem of finding a vector $(a_1,\dots,a_n)\in \mathbb{Z}^n$ ...

I am trying to write an assay about Non Interactive Zero-Knowledge proofs and would like to take the simple discrete logarithm problem example fallowing the Feige-Fiat-Shamir heuristics.
I understand ...

The most common groups to be used as examples for the DH protocol are modular multiplication and elliptic curves. But I've realised that the groups doesn't need to be finite, a suitable infinite group ...

Pollard's Rho is usually constructed using a function $f:G \rightarrow G$ which behaves 'random enough' in order to detect a collision with Floyd's cycle detection trick. It is easy enough to observe, ...

Assume that we are given an element $g\in \mathbb{F}_{p^n}^*$ and $g$ does not belong to any of the smaller subfields contained in $\mathbb{F}_{p^n}$. If the degree of $g$ is some number $q$, how much ...

It is well known how to produce a NIZK that curvepoints $aG$ and $aP$ have the same discrete logarithm $a$ with respect to the curvepoints they are multiplied by. There is also a way to prove that a ...

I'm one of the developers of an application which uses SRP-6 as the authentication mechanism. The authentication part of the code is very old and uses N with only 256 bits (all arithmetic is done in ...

I have a question about the Pohlig-Hellman Algorithm for the discrete log problem. I understand the concept, but doing the exact calculations I get confused at one point; to illustrate, let's look at ...

I saw this awesome video which shows how encryption works using "discrete logarithm".
The example says: $3^x\mod17$. I understood that $3$ is called “generator”, because it has no "straight" root and ...

Suppose there are two elements $a = g^x$ and $b = h^x$, where $g$ and $h$ are generators in $Z^*_p$ and $p$ is a large prime. How can we prove that $a$ and $b$ have the same discrete logarithms with ...

We have a multiplicative cyclic group $G$ which is a subgroup of $(\mathbb{Z}/n\mathbb{Z})∗$. There are two parties, Alice and Bob:
If:
Alice knows: $b$ and $x$ such that $x^x = b$;
Bob knows: $b$.
...